Sec. 7. A candidate for the office of United States Senator in a special election held to fill a vacancy in accordance with IC 3-13-3-1 shall be nominated:
(1) at a primary election held under IC 3-10-1, if the vacancy occurs no later than noon on the first date that a petition of nomination can be filed with a county voter registration office under IC 3-8-2-10 before the primary election;
(2) as provided in IC 3-13-1-3, if the vacancy occurs after noon on the first date that a petition of nomination can be filed with a county voter registration office under IC 3-8-2-10 before a primary election held under IC 3-10-1; or
(3) under IC 3-8-6, if a candidate is an independent candidate or represents a political party not qualified to nominate candidates at a primary election.